integral of (3x^5-8x^3+2)

解答

\int (3 x^{5} - 8 x^{3} + 2) d x

\frac{x ^{6}}{2} - 2 x^{4} + 2 x + C

求解步骤

\int 3 x^{5} - 8 x^{3} + 2 d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 x^{5} d x - \int 8 x^{3} d x + \int 2 d x

\int 3 x^{5} d x = \frac{x ^{6}}{2}

\int 8 x^{3} d x = 2 x^{4}

\int 2 d x = 2 x

= \frac{x ^{6}}{2} - 2 x^{4} + 2 x

解答补常数

= \frac{x ^{6}}{2} - 2 x^{4} + 2 x + C

\int \frac{( x ^{3} - x ^{4} ) ^{2}}{x} d x

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